Molecular Spectroscopy For UG and PG Students Part 2.pptx

General Molecular Spectroscopy for UG and PG Students. Part-II

1. Shri Shivaji Education Society Amravati’s Shri Shivaji Arts, Commerce & Science College Motala , Dist. Buldana

2. Molecular Spectroscopy Part-2 By Mr. Bhaskarrao Subhashrao Bhise Assistant Professor Head Department of Chemistry Shri Shivaji Arts, Commerce & Science College Motala Dist. Buldana

3. Contents Energy Level Diagram of Transitions Rotational ( Microwave) Spectroscopy Condition for Microwave Active M olecules Expression for Moment of Inertia Selection Rule for Rotational Transition Isotopic Effect

4. 1. Energy l evel diagram of a molecule indicating electronic, vibrational and rotational transitions:- Molecules absorb band spectrum under high resolution. It is found that band contains large number of fine lines The molecule can process discrete values of rotational, vibrational and electronic energies. The group of energy designated by quantum number ‘n’ is the energy level of molecule. Similarly vibrational energy are given by vibrational quantum energy ‘v’. Rotational energy designated by rotational quantum number ‘j’, shown in the diagram.

5. V=0 V=1 V=2 V=3 V=4 V=0 V=1 V=2 V=3 V=4 ENEGRY J=0 J=1 J=2 J=0 J=1 J=2 4321 4321 B A C D Electronic Transition Vibrational Transition Rotational Tran. Each electronic energy level contain several vibrational energy levels and each vibrational energy level contain several rotational level. ΔE (Electronic) >> Δ E (Vibrational) >> Δ E( Rotational).

6. 1. Rotational Transition:- When a molecule absorb electromagnetic radiation nearly 0.005ev, the molecule is excited from lower rotational level to higher energy level. The selection rule, Δ j=+1. The branch of molecular spectroscopy involving rotational transitions only called as rotational or microwave spectroscopy. 2. Vibrational Transitions:- 1. When a molecules absorb electromagnetic radiation nearly 0.1ev, the molecule excited from lower level to higher energy level. 2. The selection rule for this transition Δ v =+1. 3. A branch of spectroscopy involving vibrational transition is called as vibrational transition. 3. Electronic Transition:- When molecule absorb energy nearly 50 to 100 ev , then there is an electronic transition from lower ( ground state) energy level to higher ( excited state) energy level.

7. Rotational ( Microwave) Spectroscopy:- When electromagnetic radiation supply energy, molecule absorb microwave region energy, then only rotational transition occurs. Microwave absorption spectrum of a molecule consist of equally discrete lines. Condition for microwave active molecules:- Molecules having capability of absorbing microwave radiation are called as microwave active molecules. Microwave active molecules having permanent dipole moment. i.e. molecule must be polar. Hetero diatomic molecule like NO, CO, HCl, HBr , HF etc are active. Mononuclear diatomic molecules like H2, O2, N2, Cl2, F2 etc are microwave inactive because these are non-polar molecules.( μ =0). For microwave active spectrum must be molecule in gaseous state because of condensed state ( solid or liquid) rotational energy very close to each other and hence spectrum can not recorded. HCl(gas) gives rotational spectrum but HCl(liquid) can not record spectrum.

8. Expression for Moment of inertia of a diatomic rigid rotator:- Consider diatomic molecule AB. Let atom A (mass=m1) and B (mass=m2) are fixed in position and molecule rotating about axis passing through the center of gravity “G”. A B r 1 r 2 m 1 m 2 G r Let r is internuclear distance ( Bond length) and r 1 & r 2 are distance of atom A and B respectively from center of gravity (r 1 + r 2 = r ). As the system is balanced about its centre of gravity (G). m 1 r 1 = m 2 r 2 M 1 r1 = m2( r -r 1 ) M 1 r 1 = m2r – m 2 r 1 M 2 r = m 1 r 1 + m 2 r 1 M 2 r = r 1 (m 1 + m 2 ) r 1 = ------------ (1)   Similarly r 2 = ------------ (2)  

9. Moment of inertia ( I ) of molecule AB is given by r 1 = ------------ (1) I = m 1 r 1 2 + m 2 r 2 2 -------------( 3) r 2 = ------------ (2) Substituting the values of r1 and r2 in equation (3) , we get I = m1 2 + m2 2 I = + I = I = x r 2 = μ r 2 Where, μ is the reduce mass of diatomic molecule and its value is μ=  

10. Rotational Spectrum of Diatomic Rigid Rotator:- Rotational energy ( Ej ) of diatomic rigid rotator is obtained by solving Schrondinger wave equation and given by Ej = J(J+1) where, J= rotational quantum number J=0, 1, 2, 3 --------, h= planks constant and I= moment of inertia In microwave spectroscopy, position of lines usually expressed in cm -1 and hence rotational energy ( j) in cm -1 , which is given by j= = J(J+1) j= J(J+1) cm -1 [h= js , I= kgm 2 , c= cm/s ] = BJ ( J+1) cm -1 , where J=0, 1, 2, -----, and B= cm -1 For a given molecule‘ B’ is constant and is called as rotational constant of the molecule  

11. The value of rotational energy (   Rotational Quantum Number (J) Rotational energy ( J=O =0 J=1 =2B J=2 =6B J=3 3 =12B J=4 =20B J=5 30B Rotational Quantum Number (J) J=O J=1 J=2 J=3 J=4 J=5 Ex.1 J=O Ex.2 J=1 =BJ (J+1) =BJ (J+1) =0 (0+1)B = 1 (1+1)B =0 =2B Ex.3 J=2 Ex.4 J=3 Ex.5 J=4 = BJ (J+1 ) = BJ (J+1 ) =BJ (J+1) =2 ( 2+1)B =3 (3+1)B = 4 (4+1)B =6B = 12B = 20B J=3 J=2 J=1 J=0 2B 6B 12B Energy Rotational energy level diagram

12. Selection Rule for Rotational Transitions Only those rotational transition allowed for which Δ J=+1 for absorption of spectrum and Δ J=-1 for emission of spectrum. In microwave spectroscopy, usually Δ J=+1 study the absorption spectrum.   Origin of line in the Rotational Spectrum of diatomic rigid rotator:- According to selection rule, the absorption of spectrum transition arises from lower level to higher level ( Δ j= +1). Allowed transition and lines are shown in the table. Line Number Allowed Rotational Transition ( Δ j=+1) Position of absorption lines ( cm -1 ) First Line J=o j=1 Position= =2B-0 =2Bcm -1 Second Line J=1 j=2 Position= =4Bcm -1 Third Line J=2 j=3 =6Bcm -1 Fourth Line J=3 j=4 Position= Line Number Allowed Rotational Transition ( Δ j=+1) Position of absorption lines ( cm -1 ) First Line J=o j=1 Second Line J=1 j=2 Third Line J=2 j=3 Fourth Line J=3 j=4

13. The position of spectral lines obtained by deriving following equation Suppose molecule absorb energy which obtained rotational transition from lower energy level J ’ to higher energy level J. Therefore lower energy given by, EJ’= J’(J’+1) And higher energy level given by, EJ = J(J+1) The difference between two levels given by ΔEr = E J -E J’ = = J’ 2 -J’] = J ’) + (J-J’)] = J ’) (J-J’) + (J-J ’)] = J’) (J+J’+1)] --------------------(1) According to selection rule for rigid rotator diatomic molecule value J change only only one unit. Therefore ΔJ= J-J’ =  

14. If molecule jump from lower energy level to higher energy level, then Δ J= +1. If transition from higher level to lower level , then Δ J=-1 For absorption, ⁖ J-J’=+1 J’=J-1 E J -E J’ = [+1(J+J-1+1) = (2J) = J But ΔE= h ⊽c h ⊽c = J ⁖ ⊽= J = 2 J = 2B. J ---------------(2) Where, B = This gives frequency of radiation absorbed in term wave number the value of J= 1, 2, 3, …., in eq.2  

15. The frequency of spectral lines come out to be 2B, 4B, 6B etc. It means that spacing between lines is equal to ( 2B). This is called frequency separation. Frequency separation(2B) = Absorption rotational spectrum of rigid rotator as shown in figure. 2B 4B 6B 8B 10B 2B 2B 2B 2B ⊽ 1 ⊽ 2 ⊽ 3 ⊽ 4 ⊽ 5 Fig. Absorption rotational spectrum of diatomic rigid rotator.   It is clear that the on above figure and derivation lines in absorption rotational spectrum of diatomic rigid rotator are equal spaced and separated by 2B cm -1

16. Isotope Effect Same atomic number but different atomic mass called as isotope. If hetero diatomic molecule ( AB) is substituted by isotope of same element with higher mass number ( A’B) then position of absorption spectra of two molecules will be different. This phenomenon called as isotope effect. Isotope ( A’B) will have higher reduce mass than AB. μ = Bond length ( r ) is same for both. A’B will have high moment of inertia than AB. Rotational constant is inversely proportional to the moment of inertia. Rotational constant of A’B will lower than of AB. Rotational spectra of two these molecules shown in figure. 2B 4B 6B 8B 2B 2B AB Molecule 2B 2B’ 4B’ 6B’ 8B’ 2B 2B AB’ Molecule 2B  

17.   Application of Microwave Spectroscopy:- Determination of moment of inertia ( I) of the diatomic molecule:- Recorded spectra spacing between lines ( 2B) is calculated . From this I is calculated using formula I = Where, h= 6.62 x 10 -34 , ᴨ = 3.14 , B = in m -1 C = 3 x 10 8 ms -1 , I = in kg m 2 2. Determination of bond length ( r ) for diatomic molecules:- First calculated moment of inertia from recorded spectra. Then calculated reduce mass ( μ ) of molecule from atomic mass. μ = Finally, bond length calculate using formula. I = μ r 2 r 2 = r =  

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